Answer:
- discriminant: 11
- solutions: -6, +5
Step-by-step explanation:
Comparing your equation to the standard form, we can find the values necessary to compute the discriminant:
x^2 +x -30 = 0
ax^2 +bx +c = 0
So, we have ... a = 1, b = 1, c = -30
The discriminant is defined as ...
d = √(b² -4ac) = √(1² -4(1)(-30)) = √121
d = 11
The solutions are ...
x = (-b ± d)/(2a) = (-1 ±11)/2
x = {-6, +5}
<span>a. How many students participated?
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A = (1/2) b * h
h = b - 5
42 = (1/2) * b * (b - 5)
42 = (1/2) * b^2 - 5b
multiply both sides by 2 to clear the fraction (1/2)
2(42) = 2(1/2) *b^2 - 5b
84 = b^2 -5b
Since this is a quadratic equation, subtract 84 from both sides so that it is set = to zero.
b^2 - 5b - 84 = 0
Now factor.
(b - 12)(b + 5) = 0
b - 12 = 0; b = 12
b + 5 = 0; b = -5
You can't have a negative length so the answer is 12m
To check the answer:
A = (1/2) * 12* 7
A = 42 m^2
4 equal sides, 4 right angles, 2 pairs of parallel and opposit sides I think